On the spectrum of narrow Neumann waveguide with periodically distributed $δ'$ traps

Pavel Exner; Andrii Khrabustovskyi

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arXiv · 1405.1367

On the spectrum of narrow Neumann waveguide with periodically distributed $δ'$ traps

Pavel Exner·Andrii Khrabustovskyi

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Abstract

We analyze a family of singular Schrödinger operators describing a Neumann waveguide with a periodic array of singular traps of a $δ'$ type. We show that in the limit when perpendicular size of the guide tends to zero and the $δ'$ interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.

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BibTeX RIS

Pavel Exner, Andrii Khrabustovskyi. 2014-05-06. On the spectrum of narrow Neumann waveguide with periodically distributed $δ'$ traps. https://arxiv.org/abs/1405.1367

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